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Mirrors > Home > ILE Home > Th. List > sbcbi2 | Unicode version |
Description: Substituting into equivalent wff's gives equivalent results. (Contributed by Giovanni Mascellani, 9-Apr-2018.) |
Ref | Expression |
---|---|
sbcbi2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | abbi 2251 | . . 3 | |
2 | eleq2 2201 | . . 3 | |
3 | 1, 2 | sylbi 120 | . 2 |
4 | df-sbc 2905 | . 2 | |
5 | df-sbc 2905 | . 2 | |
6 | 3, 4, 5 | 3bitr4g 222 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1329 wceq 1331 wcel 1480 cab 2123 wsbc 2904 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-11 1484 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-sbc 2905 |
This theorem is referenced by: csbeq2 3021 |
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